Problem: Simplify the following expression: $r = \dfrac{1}{7k} - \dfrac{1}{5k}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7k$ and $5k$ $\lcm(7k, 5k) = 35k$ $ r = \dfrac{5}{5} \cdot \dfrac{1}{7k} - \dfrac{7}{7} \cdot \dfrac{1}{5k} $ $r = \dfrac{5}{35k} - \dfrac{7}{35k}$ $r = \dfrac{5 -7}{35k}$ $r = \dfrac{-2}{35k}$